US11577384B2 - Brake path monitoring of a kinematic - Google Patents

Brake path monitoring of a kinematic Download PDF

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Publication number
US11577384B2
US11577384B2 US16/386,714 US201916386714A US11577384B2 US 11577384 B2 US11577384 B2 US 11577384B2 US 201916386714 A US201916386714 A US 201916386714A US 11577384 B2 US11577384 B2 US 11577384B2
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point
braking
envelope
region
kinematic
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US20190321975A1 (en
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Thomas DIRSCHLMAYR
Thomas KAPELLER
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ABB Schweiz AG
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B&R Industrial Automation GmbH
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B25J9/1666—Avoiding collision or forbidden zones
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1671—Programme controls characterised by programming, planning systems for manipulators characterised by simulation, either to verify existing program or to create and verify new program, CAD/CAM oriented, graphic oriented programming systems
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1674—Programme controls characterised by safety, monitoring, diagnostic
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1674—Programme controls characterised by safety, monitoring, diagnostic
    • B25J9/1676—Avoiding collision or forbidden zones
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1692—Calibration of manipulator

Definitions

  • the present invention relates to a method for controlling a kinematic that is modelled in a kinematics coordinate system by means of hingedly interconnected single axles, at least one of the single axles being connected to an origin of the kinematics coordinate system and at least one of the single axles moving relative to the origin.
  • kinematics Since manufacturing processes in the field of robotics are intended to be achieved in increasingly small spaces, the fields of operation of robots (also referred to, in a general manner, as kinematics) often overlap with those of other objects such as fixed installations, robots, machines or people.
  • Kinematics is understood both as serial kinematics and parallel kinematics, but also mixtures thereof, a serial or parallel kinematic comprising, in a known manner, a number of joints that are interconnected, in series or in parallel, by means of rigid connecting elements (e.g. tripod or hexapod).
  • rigid connecting elements e.g. tripod or hexapod
  • working regions and/or safety regions which kinematics, or portions thereof, may not leave or may not pass, are often defined in a kinematics working space. Protection for people and objects has to be ensured, in particular owing to high and increasing safety requirements.
  • a brake path of a kinematic during operation should also be taken into account. If a braking process is initiated at a braking time, the joints and arms of the robot continue to move until they remain in an end position. It is necessary to ensure that, when braking is initiated, the unavoidable braking movement of the kinematic never results in working spaces being left and safety regions being entered.
  • a known approach for taking account of the brake path is that of assuming a circle or a sphere as a possible brake path, the radius of the circle or sphere resulting from the sum of the possible individual brake paths of single axles.
  • the object of the present invention is therefore that of specifying a method for controlling a kinematic, braking regions that may be covered by the kinematic during a braking process being calculated with a high degree of precision and efficiency.
  • At least one virtual end position of the point is determined from an initial position of the point, a vectorial speed of at least one single axle, and a minimum deceleration of at least one single axle, the extent of an envelope being calculated from the initial position and the at least one virtual end position.
  • a braking region of the point is determined using the envelope of the initial position and the at least one end position, and the braking region is taken into account when controlling the kinematic.
  • “Vectorial speed” means that the direction of the speed is also taken into account, in addition to the magnitude of the speed, the vectorial speed corresponding to the initial speed when the braking process is initiated.
  • a vectorial speed of a moving revolute joint axle can be described as the angular speed along an associated axis of rotation, and a vectorial speed of a prismatic joint axle can be described as the speed along an associated thrust axis.
  • the determined virtual end position of course generally does not correspond to the actual end position of the point after the braking process, it nonetheless being possible for the point to reach the virtual end position if the relevant single axle is actually decelerated at the minimum deceleration and if no further single axles are involved in the movement or in the braking process.
  • the minimum deceleration may be specified or calculated, and describes the deceleration at which the at least one single axle can be guaranteed to be decelerated during the braking process. This thus ensures that the point is guaranteed to come to a halt within the determined braking region.
  • the minimum deceleration can be determined from the dynamic properties of portions of the kinematic, for example the mass of a single axle, both during operation of the kinematic and in advance.
  • the minimum deceleration can also be specified in advance or during operation, e.g. as an external parameter, etc.
  • the deceleration of the at least one single axle counteracts the speed of the at least one single axle, and is thus a negative acceleration directed counter to the speed.
  • the minimum deceleration of the single axle in question results, at the braking time, from an available braking torque, the load, etc., may also be related to the current speed, etc., or may also be known in advance.
  • a specified minimum deceleration for a particular load of the kinematic can be derived from a datasheet for example.
  • a lower value may be assumed for the minimum deceleration used in the method than the value for the specified minimum deceleration.
  • no kinematic object is modelled as a three-dimensional geometric body.
  • at least one end position of a point of the kinematic can be considered to be the object to be monitored, the kinematics being modelled by means of a number of single axles (linear, i.e. one-dimensional objects) which for example each connect two kinematic objects, e.g. joint hubs (punctiform, i.e. zero-dimensional objects).
  • the point considered may be located on a modelled single axle or on a kinematic object of the kinematic, but must at least be coupled to a single axle, e.g. move together with a single axle.
  • the point may be located outside the kinematic (modelled by single axles and kinematic objects).
  • the braking process is initiated at a braking time, at which the point is in the initial position.
  • At least one virtual end position of the point is determined from the vectorial speed and the specified minimum deceleration of at least one single axle, and at least one braking vector can be determined from the initial position and the at least one virtual end position.
  • the envelope is a two-dimensional or three-dimensional object that bounds the at least one determined braking vector.
  • the envelope can exactly bound the at least one braking vector, although this is expedient only if the at least one braking vector does not or cannot deviate from the virtual partial movement of the point during the braking process. This situation occurs for example if just one braking vector is present which is in addition formed by the movement of just one prismatic joint axle.
  • the extent of the envelope E can be calculated from the initial position, the at least one virtual end position, and a virtual partial movement resulting therefrom.
  • a virtual partial movement is understood to be a possible trajectory which is determined, within the context of the method according to the invention, from the virtual end position, using the minimum deceleration.
  • the actual trajectory as the actual movement path of the point during the braking process is, of course, unknown, inter glia because the deceleration that actually occurs is usually not known.
  • the virtual partial movement of the point can generally not be considered a straight link from the starting point to the end point.
  • the actual trajectory, as well as the actual end position, is not known.
  • the envelope can, however, be selected such that all trajectories that may occur during the braking process are bounded by the envelope if, as is assumed, the minimum deceleration is adhered to.
  • the virtual partial movements can then be calculated, proceeding from the starting point and at least one end point, and the envelope can be designed so as to bound all virtual partial movements as precisely as possible. This can result in complex geometries for the envelopes, which usually results in significant computational effort, but this can be kept low by means of suitable algorithms.
  • simple geometric shapes such as rectangles (in two-dimensional space) or cuboids (in three-dimensional space) can also be determined as the envelope, which shapes are calculated from the starting point and at least one end point (and must of course always bound the starting point and associated at least one end point or the virtual partial movements), as will be described in the following.
  • At least one virtual end position of the point is determined from the initial position of the point, a vectorial speed of each single axle moved, and a minimum deceleration of each single axle moved.
  • the movement, i.e. the vectorial speed and the minimum deceleration, of each single axle is directly taken into account when determining the virtual end position.
  • the vectorial speed of the point thus results as a linear combination of vectorial speeds of the single axles that are moved.
  • At least one virtual end position of the point is determined from the vectorial speed and the specified minimum deceleration of at least one (or of each) single axle. It is possible, however, for at least one braking vector, which connects the initial position to the at least one virtual end position, to be determined, and for the extent of an envelope to be calculated from the at least one braking vector.
  • the envelope can exactly bound the at least one braking vector, although this is expedient only if the at least one braking vector does not or cannot deviate from the virtual partial movement of the point during the braking process. This situation occurs for example if just one braking vector is present which is in addition formed by the movement of just one prismatic joint axle.
  • the braking vectors can advantageously be formed by a linear combination of basis braking vectors, each basis braking vector being assigned to one single axle and connecting the initial position of the point to an associated virtual end position of the point, the associated virtual end position of the point being determined from the initial position of the point, a vectorial speed of the assigned single axle, and the minimum deceleration of the assigned single axle, the assumption being made, for each basis braking vector, that the non-assigned single axles do not move any further.
  • the possible trajectory of the point is split into individual virtual partial movements. The end position of a point that follows a virtual partial movement of this kind corresponds to the virtual end position.
  • the virtual partial movements quasi cover the “worst case” situation, since they are determined on the basis of the minimum deceleration.
  • the braking region is determined by combining the individual virtual partial movements and corresponds to the region in which the actual trajectory would definitely be located, of course always assuming that at least the minimum deceleration is effective.
  • the extent of the envelope is approximated, according to the invention, from the braking vectors, the envelope ideally bounding all the virtual partial movements of the point such that the extent of the envelope is as small as possible.
  • At least some of the single axles may be formed as prismatic joint axles.
  • a virtual partial movement of a point describes a straight line, when the point considered is coupled to the relevant prismatic joint axle or is coupled to a single axle that is connected to the prismatic joint axle.
  • the vectorial speed of a prismatic joint axle thus acts along said straight line.
  • Said virtual partial movements thus correspond to the (basis) braking vectors when the single axle is decelerated at the minimum deceleration, and therefore it would be trivial to determine the virtual partial movement from the braking vectors.
  • the trajectory of the point actually described during the braking process could also be shorter if the single axle is braked at a deceleration greater than the minimum deceleration.
  • determining an envelope having the smallest possible extent may nonetheless require increased effort.
  • at least some of the single axles may be formed as revolute joint axles, with the result that it is not sufficient to consider braking vectors alone, because, on the basis of just this one revolute joint, the actual movement of the point is a circular arc.
  • the vectorial speed of a revolute joint axle thus acts along said circular arc.
  • the braking vector and circular arc accordingly differ by a circular segment. It would be fundamentally very complex to take account of this deviation in an arithmetically exact manner.
  • At least one further virtual end position of the point is determined for the point, from the initial position, the vectorial speed of the at least one single axle, and at least one further deceleration of the at least one single axle that is greater than the minimum deceleration of the at least one single axle.
  • the braking region of the point is determined using an envelope of the initial position and the at least one end position and the at least one further end position, the extent of the envelope being calculated from the initial position, the at least one end position, and the at least one further end position.
  • the envelope may also cover a wider region that is easier to calculate.
  • braking vectors are calculated, although it would always also be possible, in each case, to use the initial position and the at least one virtual end position instead of a braking vector.
  • the envelope can thus be determined from the virtual partial movement and can advantageously exactly bound said partial movement.
  • the envelope can thus advantageously be calculated on a first rectangle that corresponds to a minimum bounding rectangle of the braking vectors or of the initial position and virtual end positions, and the sides of which rectangle are preferably in parallel with the kinematics coordinate system.
  • the envelope can also be calculated, in an analogous manner, on a first cuboid that constitutes a minimum bounding cuboid of the braking vectors or of the initial position and virtual end positions, and the sides of which cuboid are in parallel with the kinematics coordinate system, which may be advantageous in order to consider the kinematic in three-dimensional space.
  • the minimum bounding cuboid or the minimum bounding rectangle bounds only the braking vectors, or the initial position and virtual end positions, which, as mentioned, may deviate from the virtual partial movements when revolute joint axles are used.
  • the first rectangle or the first cuboid may therefore be expanded, by a preferably direction-independent correction value which at least takes account of the deviation of the braking vectors from the virtual partial movements of the point from the initial position into the respective virtual end positions, to an expanded first rectangle or a first expanded first cuboid.
  • the envelope is furthermore likewise expanded on the expanded first rectangle or the first expanded first cuboid.
  • the deviations of the virtual partial movements from the braking vectors in the form of the height of the respective circular sectors, can be added to the length and width of the rectangle in order to expand said rectangle to an expanded first rectangle.
  • the correction value can also take account of direction-independent brake path portions, preferably position tolerances of the single axles.
  • the correction value can also take account of direction-independent brake path portions which result from anticipated deviations between the calculated and the actual position. Said anticipated deviation can in turn result from known error response times, difference quotients, discretization errors, extrapolation inaccuracies, calculation inaccuracies, encoder and/or coupling resolutions, offset errors, mechanical deformations, etc.
  • a safety region of the kinematic can be expanded by means of the envelope and/or a working region of the kinematic can be reduced by means of the envelope, resulting in a modified safety region or a modified working region.
  • the first rectangle or the first cuboid is expanded, by a correction value which at least takes account of the deviation of the braking vectors from the virtual partial movements of the point from the initial position into the respective virtual end positions, to an expanded first rectangle or a first expanded first cuboid, a safety region of the kinematic and/or a working region of the kinematic being provided in a working space using a working space coordinate system, the envelope being expanded to a second expanded rectangle or a second expanded cuboid, the sides of which touch the corners of the first expanded rectangle or of the first expanded cuboid and are in parallel with the working space coordinate system, and a safety region of the kinematic being expanded by means of the envelope and/or a working region of the kinematic being reduced by means of the envelope, resulting in a modified safety region or a modified working region.
  • the adjustment of the working region to the reduced working region or of the safety region to the expanded protection region using the envelope can take place in a suitable
  • the initial position of the point can advantageously be moved along the boundaries of the safety region or of the working region, and the modified safety region can be formed by the total of the safety region and envelope, and the modified working region can be formed by the difference between the working region and the envelope.
  • the envelope is thus applied to the working space to be monitored (permitted working region or forbidden safety region).
  • the working space is increased (in the case of the safety region) or reduced (in the case of the working region).
  • it is not necessary to calculate any intersection points of two two-dimensional geometric bodies but instead simply the intersection point between a point (kinematic object) or a line (single axle) and a zero-, one-, two- or three-dimensional working region.
  • the kinematic itself is thus not modified, and therefore a kinematic object does not need to be treated as a two-dimensional or three-dimensional object.
  • the modified safety region or the modified working region can in addition be monitored, and an action can be taken as soon as the point enters the modified safety region or the point leaves the modified working region.
  • Deactivation of the kinematic, outputting of a warning signal, etc. may function as the action.
  • the method according to the invention can of course also be used for a plurality of points of the kinematic, and advantageously for at least one point per single axle.
  • the braking vectors and, therefrom the envelope can be determined in each case for each point.
  • associated working regions or safety regions can be modified for each point.
  • FIGS. 1 to 6 C schematically show advantageous embodiments of the invention by way of example and in a non-limiting manner.
  • FIGS. 1 to 6 C schematically show advantageous embodiments of the invention by way of example and in a non-limiting manner.
  • FIG. 1 shows a kinematic formed of three single axles
  • FIG. 2 A-H show the single axles in the initial position and in the end positions
  • FIG. 3 shows braking vectors of a point
  • FIG. 4 A , B show a virtual partial movement of the point in the form of a circular arc
  • FIG. 5 A shows an envelope expanded to a first rectangle
  • FIG. 5 B shows an envelope expanded using a correction value
  • FIG. 6 A shows an envelope transformed in a working space
  • FIG. 6 B shows a modified safety region
  • FIG. 6 C shows a modified working region
  • FIG. 1 shows a part of a kinematic 1 , in this case a serial kinematic, as a one-dimensionally modelled part of a robot arm.
  • a simplified form of a wire frame model is used to model the kinematic 1 .
  • the kinematic 1 is modelled by three punctiform kinematic objects O 1 , O 2 , O 3 in a kinematics coordinate system CGS, the first kinematic object O 1 and the second kinematic object O 2 each constituting joint hubs of the robot arm.
  • Three single axles Q 1 , Q 2 , Q 3 of the kinematic 1 form a kinematic chain and connect the kinematic objects O 1 , O 2 , O 3 to an origin CGS 0 of the kinematics coordinate system CGS, along the kinematic chain.
  • the third kinematic object O 3 could for example be a connection point for a further single axle.
  • the first single axle Q 1 connects the origin CGS 0 to the first kinematic object O 1
  • the second single axle Q 2 connects the first kinematic object O 1 to the second kinematic object O 2
  • the third single axle Q 3 connects the second kinematic object O 2 to the third kinematic object O 3
  • a control unit 2 (hardware and/or software) ensures the movements of the single axles Q 1 , Q 2 , Q 3 via control lines 21 , 22 , 23 , which single axles may in principle be designed as revolute joint axles or prismatic joint axles. In this case, the single axles Q 1 , Q 2 , Q 3 can move relative to the origin CGS 0 .
  • the first single axle Q 1 and the third single axle Q 3 are revolute joint axles, which is symbolized by the arrows transverse to the single axle Q 1 , Q 3 . Since the first kinematic object O 1 moves in a relative manner together with the first single axle Q 1 , the first kinematic object O 1 is pivoted along a circular path or a circular arc when the first single axle Q 1 is moved in relation to the origin CGS 0 . In this case, the first single axle Q 1 covers a circle or a circular sector.
  • the third single axle Q 3 can pivot the third kinematic object O 3 , connected thereto, along a circular arc in relation to the second kinematic object O 2 , while the third single axle Q 3 moves along a circular sector with respect to the second kinematic object O 2 .
  • the possible movements of the single axles Q 1 , Q 3 formed as revolute joint axles are generally restricted to a region of action and can therefore in each case move along a circular sector. If there is no restriction to a region of action, for example if deceleration occurs gradually during a braking process and/or the speed v 1 , v 2 , v 3 is very high, a revolute joint axle would cover a complete circle.
  • the second single axle Q 2 is formed as a prismatic joint axle, which is indicated by the double arrow in parallel with the second single axle Q 2 , and allows the second kinematic object O 2 to move along a straight line in relation to the first kinematic object O 1 , over which line the prismatic joint axle can extend and retract.
  • the movements of single axles Q 1 , Q 2 , Q 3 can of course change the position of single axles Q 1 , Q 2 , Q 3 connected thereto.
  • a rotation of the first single axle Q 1 of course also brings about a rotation of the second single axle Q 2 and of the third single axle Q 3 , etc.
  • the origin CGS 0 is assumed to be fixed and thus describes the position of a movably mounted joint hub, making a movement of the first single axle Q 1 and of the following coupled second and third single axle Q 2 , Q 3 possible.
  • a braking process is initiated at a braking time, the single axles Q 1 , Q 2 , Q 3 continuing to move until they reach a standstill.
  • the single axles Q 1 , Q 2 , Q 3 are at known initial positions p 1 a , p 2 a , p 3 a in each case, and each move at a known speed v 1 , v 2 , v 3 , an angular speed of course also being assumed as the speed in the case of revolute joint axles.
  • the first single axle Q 1 moves from a first initial position p 1 a to a first end position p 1 e
  • the second single axle Q 2 moves from a second initial position p 2 a to a second end position p 2 e
  • the third single axle Q 3 moves from a third initial position p 3 a to a third end position p 3 e
  • a specified or calculated minimum deceleration a 1 , a 2 , a 3 counteracting the relevant speed v 1 , v 2 , v 3 in each case, the speed v 1 , v 2 , v 3 of course being understood to be the initial speed at the start of the braking process.
  • the associated speed v 1 , v 2 , v 3 of course reduces during the braking process.
  • the decelerations a 1 , a 2 , a 3 result inter alia from the inertia of the single axles Q 1 , Q 2 , Q 3 and a braking action that can be applied by the kinematic 1 , and may be known in advance or determined at the braking time.
  • the minimum decelerations a 1 , a 2 , a 3 result in the maximum end positions in each case as end positions p 1 e , p 2 e , p 1 e for the single axles Q 1 , Q 2 , Q 3 , at which end positions said axles are certain to come to a standstill during a braking process.
  • the single axles Q 1 , Q 2 , Q 3 could also be braked more rapidly than at the minimum deceleration a 1 , a 2 , a 3 , and theoretically even immediately (i.e. by an infinitely great deceleration a 1 , a 2 , a 3 ).
  • At least one virtual end position p 1 , . . . , p 7 of the point P is determined from an initial position p 0 of the point P, a vectorial speed v 1 of at least one single axle Q 1 , Q 2 , Q 3 , and a minimum deceleration a 1 , a 2 , a 3 of at least one single axle Q 1 , Q 2 , Q 3 .
  • the third kinematic object O 3 located on the third single axle Q 3 is considered as the point P, and in the following the brake path for said point P is determined.
  • the brake path corresponds to the region that could be covered by virtual partial movements of the point P during the braking process.
  • FIG. 2 A shows the single axles Q 1 , Q 2 , Q 3 of the kinematic 1 shown in FIG. 1 in the initial position p 1 a , p 2 a , p 3 a , the point P being located in an initial position p 0 .
  • FIG. 2 H shows the end positions p 1 e , p 2 e , p 3 e of the single axles Q 1 , Q 2 , Q 3 which have all been braked at the minimum deceleration a 1 , a 2 , a 3 , the point P being located in the virtual end position p 7 .
  • the possible, different virtual end positions p 1 , . . . , p 7 of the point can each be formed by varying the decelerations of the single axles Q 1 , Q 2 , Q 3 , i.e. all the initial positions p 1 a , p 2 a , p 3 a and end positions p 1 e , p 2 e , p 3 e .
  • Virtual end positions p 1 , . . . , p 7 are then determined.
  • the virtual end positions p 1 , . . . , p 7 describe the possible end positions of the point P when a minimum deceleration a 1 , a 2 , a 3 occurs, on the basis of individual movement portions of the overall movement (e.g. only the first and second single axle Q 1 , Q 2 ).
  • the envelope E can be determined from the initial position p 0 and the virtual end positions p 1 , . . . p 7 . It is also possible, however, (see FIG. 3 ) to determine braking vectors b 1 , . . .
  • b 7 which connect the initial position p 0 to the possible (in the simplest case at least one) virtual end positions p 1 , . . . , p 7 , and to determine the envelope E using the braking vectors b 1 , . . . , b 7 .
  • the braking vectors b 1 , . . . , b 7 which are then also used for determining the envelope E can also be formed of a linear combination of basis braking vectors, each basis braking vector being assigned to a moved single axle Q 1 , Q 2 , Q 3 . It is therefore assumed, for each basis braking vector, that the basis braking vectors of non-assigned single axles Q 1 , Q 2 , Q 3 do not move any further.
  • the associated virtual end position p 1 , p 2 , p 4 of the point P is determined from the initial position p 0 of the point P, a vectorial speed v 1 , v 2 , v 3 , and the minimum deceleration a 1 , a 2 , a 3 of only the assigned single axle Q 1 , Q 2 , Q 3 .
  • the basis braking vector connects the initial position p 0 of the point P to the virtual end position p 1 , p 2 , p 4 of the point P that is associated therewith.
  • FIGS. 2 B, 2 C and 2 E The virtual end positions p 1 , p 2 , p 4 of the point P which can be used for determining the associated basis braking vectors are indicated in FIGS. 2 B, 2 C and 2 E .
  • FIG. 2 B shows, by way of example, the virtual end position p 1 in the event of the first single axle Q 1 , moved at the first speed v 1 , being braked at the minimum deceleration a 1 (not shown), immediate standstill being assumed for the second single axle Q 2 and the third single axle Q 3 , i.e. the movement of the second single axle Q 2 and of the third single axle Q 3 is not taken into account.
  • FIG. 2 C shows the virtual end position p 2 in the event of the second single axle Q 2 , moved at the second speed v 2 , being braked at the minimum deceleration a 2 (not shown), it being assumed that the first single axle Q 1 and the third single axle Q 3 come to an immediate standstill or are not moved.
  • FIG. 2 D the first single axle Q 1 and the second single axle Q 2 were braked (at the minimum deceleration a 1 , a 2 which is not shown), and immediate standstill was assumed for the third single axle Q 3 ;
  • FIG. 2 F the first single axle Q 1 and the third single axle Q 3 were braked (at the minimum deceleration a 1 , a 3 which is not shown), and immediate standstill was assumed for the second single axle Q 2 ;
  • FIG. 2 G the second single axle Q 2 and the third single axle Q 3 were braked (at the minimum deceleration a 2 , a 3 which is not shown), and immediate standstill was assumed for the first single axle Q 1 .
  • FIG. 2 D the first single axle Q 1 and the second single axle Q 2 were braked (at the minimum deceleration a 1 , a 2 which is not shown), and immediate standstill was assumed for the third single axle Q 3 ;
  • FIG. 2 F the first single axle Q 1 and the third single axle Q 3 were braked (at
  • FIGS. 2 D, 2 F, 2 G and 2 H discloses braking of the first single axle Q 1 , the second single axle Q 2 and the third single axle Q 3 at the minimum deceleration a 1 , a 2 , a 3 (not shown) in each case.
  • the virtual end positions p 3 , p 5 , p 6 , p 7 of the point P, shown in FIGS. 2 D, 2 F, 2 G and 2 H can thus also be shown as linear combinations of the virtual end positions p 1 , p 2 , p 4 of the point P shown in FIGS. 2 B, 2 C and 2 E .
  • all possible virtual end positions p 1 , . . . p 7 of the point P of the kinematic 1 during braking are determined.
  • the single axles Q 1 , Q 2 , Q 3 are assumed, proceeding from the initial positions p 1 a , p 2 a , p 3 a , and the single axles Q 1 , Q 2 , Q 3 are each decelerated, preferably by a minimum, with the result that they reach the end positions p 1 e , p 2 e , p 3 e .
  • p 7 of the point P result from varying the end positions p 1 e, p 2 e , p 3 e . Since the virtual end positions p 1 , . . . , p 7 are determined from vectorial speeds v 1 , v 2 , v 3 and decelerations a 1 , a 2 , a 3 of the single axles Q 1 , Q 2 , Q 3 , not only the position, but instead also the movement direction, of the Q 1 , Q 2 , Q 3 is taken into account during the braking process.
  • FIG. 3 thus shows the initial position p 0 of the point P shown in FIG. 2 A and the possible virtual end positions p 1 , . . . , p 7 of the point P shown in FIG. 2 B- 2 H in combination, the resulting braking vectors b 1 , . . . , b 7 for the point P being shown.
  • the braking vectors b 1 , . . . , b 7 thus connect the initial position p 0 to the determined virtual end positions p 1 , . . . , p 7 of the point P.
  • braking vectors b 1 , . . . , b 7 are used for determining the envelope E. It would of course also be possible to determine the envelope E if the initial position p 0 and the at least one virtual end position p 1 , . . . , p 7 are used directly, without the braking vectors b 1 , . . . , b 7 .
  • the braking vectors b 1 , . . . , b 7 can be determined as linear combinations of the associated basis braking vectors.
  • b 1 would be a basis braking vector for the first single axle Q 1
  • b 2 would be a basis braking vector for the second single axle Q 2
  • b 4 would be a basis braking vector for the third single axle Q 3 ; see FIG. 2 .
  • a braking vector is formed by a virtual end position p 1 , . . . , p 7 that results only from extending a prismatic joint axle (in FIG. 3 for example the (basis) braking vector b 2 )
  • the relevant braking vector b 1 , . . . , b 7 in this case the braking vector b 2
  • the braking vector b 2 corresponds to the actual trajectory of the point P during the braking movement when the second single axle Q 2 is decelerated at the second minimum deceleration a 2 and the first and third single axles Q 1 , Q 3 are not moved.
  • a circular arc of course results as the virtual partial movement when the single axle connected thereto is moved.
  • the actual trajectory of the point P is unknown.
  • the virtual partial movements of the point P are determined on the basis of individual movements of the single axles Q 1 , Q 2 , Q 3 , articulated movements, or a combination of movements, under the effect of the minimum deceleration a 1 , a 2 , a 3 , at an initial speed v 1 , v 2 , v 3 .
  • the braking region of the point P is determined, according to the invention, by means of an envelope E.
  • the envelope E is a one-dimensional (e.g. in the case of a movement of just a prismatic joint axle), two-dimensional or three-dimensional object which bounds the determined braking vectors b 1 , . . . , b 7 and the extent of which is calculated from the braking vectors b 1 , . . . , b 7 .
  • the envelope E can thus bound exactly the family of braking vectors b 1 , . . . , b 7 , with the result that the extent of the envelope E is minimized.
  • this is expediently only if the virtual partial movements are not located outside the braking vectors b 1 , . . . , b 7 , as is the case for example in prismatic joint axles.
  • the envelope E could also be formed as the smallest bounding object of the family of possible virtual partial movements.
  • the virtual partial movements are generally unknown, they can be calculated from the braking vectors, usually with significant computational effort.
  • the virtual partial movements can also be determined by means of intermediate positions of the point P between the respective virtual end positions p 1 , . . . , p 7 , for example by means of the virtual end positions p 1 , . . . , p 7 also being connected to vectors and the envelope E being calculated therefrom.
  • a possible envelope E that bounds the virtual partial movements is shown in a dashed line in FIG. 3 .
  • a virtual partial movement of the point P deviates from the respective (basis) braking vectors b 1 , . . . , b 7 which are formed by pivoting a revolute joint axle.
  • a virtual partial movement of the point P i.e. of the kinematic object O 3 , which movement is given by way of example and which, owing to only the first single axle Q 1 being rotated, describes a circular arc, is shown in FIG. 4 A and FIG. 4 B .
  • the braking vector b 1 (a basis braking vector, since only the first single axle Q 1 was moved) connects the initial position p 0 to the virtual end position p 1 .
  • At least one virtual end position p′, p 1 ′′ of the point P can be determined from an initial position p 0 of the point P, a vectorial speed v 1 of at least one single axle Q 1 , Q 2 , Q 3 , and a further deceleration a 1 ′, a 1 ′′ of at least one single axle Q 1 , Q 2 , Q 3 , which deceleration is greater than the minimum deceleration a 1 , a 2 , a 3 .
  • a first further end position p 1 ′ which results from a first further deceleration at, and a second further end position p 1 ′′ which results from a second further deceleration a 1 ′′, are taken into account.
  • a first further braking vector b 1 ′ which connects the initial position p 0 to the first further virtual end position p 1 ′, and a second further braking vector b 1 ′′ which connects the initial position p 0 to the second further virtual end position p 1 ′′ are determined.
  • the extent of the envelope E can be calculated or approximated from the first braking vector b 1 , and the first and second further braking vectors b 1 ′, b 1 ′′.
  • the extent of the envelope E can also be calculated from the initial position p 0 , the at least one end position p 1 , and the at least one virtual end position p 1 ′, p 1 ′′ without calculating the braking vector b 1 or the at least one further braking vector b 1 ′, b 1 ′′.
  • the virtual partial movement is approximated exactly using an infinite number of infinitesimal increments of the further deceleration a 1 ′, a 1 ′′, extending from the minimum deceleration a 1 to an infinite deceleration. If few further braking vectors b 1 ′, b 1 ′′ are calculated, the deviation still present between the end positions p 1 , p 1 ′′ and the virtual partial movement must be taken into account when determining the envelope E, for example by an additional suitable expansion of the extent of the envelope E, similar to using the preferably direction-independent correction value h, which will be described below with reference to the first rectangle R 1 .
  • the envelope E can also advantageously be calculated from the braking vectors b 1 , . . . , b 7 or the initial position p 0 and virtual end positions p 1 , . . . , p 7 in that the envelope E is calculated as a first rectangle R 1 which is a minimum bounding rectangle of the braking vectors b 1 , . . . , b 7 and the sides of which rectangle are in parallel with the kinematics coordinate system CGS, as shown in FIG. 5 A .
  • the first rectangle R 1 is preferably expanded by a correction value h which at least takes account of a deviation of the braking vectors b 1 , . . . , b 7 from the virtual partial movements of the point P from the initial position p 0 into the respective virtual end positions p 1 , . . . , p 7 , to an expanded first rectangle R 1 ′ as the envelope E ( FIG. 58 ).
  • the braking vector b 1 deviates from the dashed virtual partial movement by a circular segment, shown hatched, having a circular segment height h 1 .
  • the above correction value h can be determined as the sum of all the circular segment heights h 1 .
  • the circular segment heights h 1 each describe the deviation of basis braking vectors b 1 , . . . , b 7 , assigned to revolute joint axles, with respect to the relevant circular arc-shaped virtual partial movement.
  • the circular segment height which describes the deviation of the fourth basis braking vector b 4 from the associated virtual partial movement would also have to be taken into account.
  • the envelope can be determined using the further decelerations a 1 ′, a 1 ′′ and a first rectangle R 1 comprising a minimum bounding rectangle R 1 of the braking vectors b 1 , . . . , b 7 , and/or a rectangle R 1 ′ expanded by the correction value h.
  • FIG. 5 B shows an envelope E that is a first rectangle R 1 ′ expanded by a correction value h (for example as the sum of the circular segment heights h 1 ).
  • h for example as the sum of the circular segment heights h 1 .
  • Direction-independent brake path portions can also be determined for the single axles Q 1 , Q 2 , Q 3 , which path portions can bring about movement of the single axles Q 1 , Q 2 , Q 3 in all spatial directions.
  • Direction-independent brake path portions can result, for example, on account of a position tolerance which describes a position deviation of a determined braking vector b 1 , . . . , b 7 from the actual position of the point P. Since the envelope E bounds all the braking vectors b 1 , . . . , b 7 of the kinematic 1 , the envelope E or the first rectangle R 1 can be expanded again, for example in that the correction value h is adjusted further, by taking account of the direction-independent brake path portions.
  • the envelope E can be transformed into a working space coordinate system WCS in which a working space W comprising a safety region SS of the kinematic 1 and/or a working region WS of the kinematic 1 is located.
  • the working space W, or the safety region SS and/or working region WS can advantageously be associated with just one point P, it being possible for a plurality of assigned working spaces W, or safety regions SS and/or working region WS, to be provided in each case for further points P.
  • a braking region to be composed of a plurality of points P and for a working space W, or a safety region SS and/or working region WS, to subsequently be calculated for a plurality of points P.
  • this is far more conservative and may also be more CPU-intensive.
  • the braking region is determined and the WS/SS adjusted for each relevant point P. Each point thus has a different WS/SS.
  • the safety region SS of the kinematic 1 can be expanded by means of the envelope E and/or a working region WS of the kinematic 1 can be reduced by means of the envelope E, resulting in a modified safety region SSm or a modified working region WSm.
  • the envelope E may be expanded to a second rectangle R 2 , the sides of which touch the corners of the first rectangle R 1 and are in parallel with the working space coordinate system WCS, as shown in FIG. 6 A . It is of course also possible for the first rectangle R 1 to be expanded to a first expanded rectangle R 1 ′ using the correction value h, and for the first expanded rectangle R 1 ′ to be used for determining the second rectangle R 2 .
  • the safety region can be modified in that the considered initial position p 0 of the point P is moved along the boundaries of the safety region SS and the modified safety region SSm is formed from the sum of the safety region SS and the envelope E, as is shown in FIG. 6 B .
  • the safety region SS is thus expanded by the envelope E shifted on the basis of the point P, with the result that the safety region SS is increased to the modified safety region SSm.
  • the modified working region WSm can be formed analogously, from the difference between the working region WS and the envelope E, as shown in FIG. 6 C .
  • the working region WS is reduced by the envelope E shifted on the basis of the point P, with the result that the working region WS is reduced to the modified working region WSm.
  • a point P preferably a modelled kinematic object O 1 , O 2 , O 3 , of a kinematic 1
  • the maximum virtual end positions p 1 , . . . , p 7 are determined at a (minimum) deceleration a.
  • an envelope E which bounds the initial position p 0 and the virtual end positions p 1 , . . . , p 7 is calculated.
  • braking vectors b 1 , . . . , b 7 that connect the initial position p 0 to the respective virtual end positions p 1 , . . .
  • a first rectangle R 1 that bounds the braking vectors b 1 , . . . , b 7 or the initial position and the virtual end positions p 1 , . . . , p 7 may be formed, and optionally expanded by a correction value h.
  • the correction value h can take account of the deviation of the braking vectors b 1 , . . . , b 7 from the virtual partial movements, as well as direction-independent brake path portions, etc.
  • the envelope E can furthermore be transformed into a working space coordinate system WCS and used for adjusting working regions WS or safety regions SS.
  • a kinematic usually allows for a three-dimensional movement.
  • the determination according to the invention of the braking region of a point P of the kinematic can be easily expanded to the three-dimensional case.
  • cuboids can be used in three-dimensional space in order to represent the envelope E.
  • the method according to the invention can of course be used for a plurality of points P of the kinematic 1 .
  • at least one point P per single axle Q 1 , Q 2 , Q 3 is considered, furthermore for each point P, according to the invention braking vectors b 1 , . . . , b 7 or an initial position and virtual end positions p 1 , . . . , p 7 , an envelope E determined therefrom, and optionally further working regions WS or safety regions SS, being modified for each point P.

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Regulating Braking Force (AREA)
  • Numerical Control (AREA)
  • Manipulator (AREA)
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CA3040608A1 (en) 2019-10-18
US20190321975A1 (en) 2019-10-24
CN110385716A (zh) 2019-10-29
CN110385716B (zh) 2024-03-12
KR20190121711A (ko) 2019-10-28

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